An archaeologist at a dig sets up a coordinate system using string. Two similar artifacts are found—one at position (1,4) and the other at (5,2) how far apart were the two artifacts? Round to the nearest tenth of a unit if necessary

The answer is composed of the following two equations

[tex]t_1 = 1[/tex] and [tex]t_n = 6*t_{n-1}[/tex]

both of these two equations combine to help form the full recursive definition

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Further explanation:

The terms are represented by the letter 't' for short. Since we have more than one term, and because we have only so many letters, this means we stick a number onto the 't' to help label multiple terms. We have t1 as the first term, t2 as the second, etc. The numbers are often show as subscripts like so [tex]t_1, t_2, t_3, \ldots[/tex]

The first term of the list of numbers is 1, so [tex]t_1 = 1[/tex] is what we start with to help set up the recursive definition.

Once we have this starting point, we use it to get to the next term which is 6. This value is 6 times the first value. Therefore, the recursive step is [tex]t_n = 6*t_{n-1}[/tex] basically saying "multiply the (n-1)st term by 6 to get the nth term. Translation:  "whatever the current term is, multiply by 6 to get the next term".

Answer: 5 feet 5 inches

Step-by-step explanation:

2 2/3 + 2 3/4 is equal to 5 5/12 so the drapes will be 5 5/12 feet long (or 5 feet 5 inches)

Answer:

The length of the drapes have to be [tex]5\frac{5}{12}\ ft[/tex]            

Step-by-step explanation:

Given : Lee needed to make Drapes the length from the floor to the top of the window the wall beneath the window had the height of [tex]2\frac{2}{3}[/tex] feet and the height of just the window measured [tex]2\frac{3}{4}[/tex] feet.

To find : How long do the Drapes have to be?

Solution :

The height of the wall beneath the window is [tex]2\frac{2}{3}=\frac{8}{3}\ ft[/tex]

The height of the window is [tex]2\frac{3}{4}=\frac{11}{4}\ ft[/tex]

The total height from the floor to the top of the window is

[tex]H=\frac{8}{3}+\frac{11}{4}[/tex]

[tex]H=\frac{32+33}{12}[/tex]

[tex]H=\frac{65}{12}[/tex]

[tex]H=5\frac{5}{12}\ ft[/tex]

Therefore, The length of the drapes have to be [tex]5\frac{5}{12}\ ft[/tex]

Answer:

Patrick earned $262.50 by mowing lawns

Step-by-step explanation:

500*0.75=375

375*.7=262.5

Answer:

$262.50

Step-by-step explanation:

It is a poorly worded question.

25 Percent of the 500 was from his birthday money.

500 * .25 = 125

That leaves 500-125 = 375

He saved 30 % of the 375 from his allowance

375 * .3 =112.50

375-112.50 =262.50

The rest is from mowing lawns.

If order matters, then there are 12 ways to do this

If order does not matter, then there are 6 ways to do this

===========================================

We have 4 choices for the first slot and 3 choices for the next (we can't reuse a letter) so that's where 4*3 = 12 comes from

If order doesn't matter, then something like AB is the same as BA. So we are doubly counting each possible combo. To fix this, we divide by 2: 12/2 = 6

To be more formal, you can use nPr and nCr to get 12 and 6 respectively (use n = 4 and r = 2)

In combinatorics, you can choose 2 letters from 4 (A, B, C, D) without replacement in 6 ways, according to the 'combination' principle in probability.

The subject of this question is combinatorics, a topic in Mathematics, particularly probability. You are asked to choose 2 letters without replacement from a set of 4 different letters {A, B, C, D}. To do this, we can use the formula for combinations, which is denoted as nCr, where n is the total number and r is the number being chosen. In this case, we can see it as 4C2.

To execute this, the formula is ‘n! / [r!(n-r)!]’ where '!' denotes factorial, meaning you multiply all natural number up to that number. Hence, 4C2 = 4! / [2!(4-2)!]. Factorial 4 (4!) = 4 * 3 * 2 *1 = 24. Factorial 2 (2!) is simply 2 * 1 = 2. Thus the calculation becomes 24 / [2*(2!)], simplifying to 24 / 4 which equals 6. So, there are 6 ways to choose 2 letters from 4 without replacement.

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Answer:

n = - 6

Step-by-step explanation:

divide both sides by 2

n + 5 = - 1 ( subtract 5 from both sides )

n = - 6

OR

distribute the parenthesis by the 2 outside

2n + 10 = - 2 ( subtract 10 from both sides )

2n = - 12 ( divide both sides by 2 )

n = - 6

Answer:

- 2      -2.5 and neither.    For the left Panel

A or 40.5 for the right panel

Step-by-step explanation:

Slope AB

Givens

(3,5) (2,7)

Formula

m = (y2 - y1)/(x2 - x1)

Solution

Slope CD

Givens

(10,5) (6,15)

Formula

m = (y2 - y1)/(x2 - x1)

Solution

What are they?

Answer: Neither.

Right Panel

The best way to start this is to plot the triangle. I use Desmos for this. See diagram below

The base is between (-6,8) and (3,8)

The 8s are the same for both points. The distance between -6 and 3 is abs(-6) + abs(3) = 9

That is the base of the triangle.

The height is between (-6,17) and (-6,8)

17 - 8 = 9    

Notice I did not have to use the absolute values. Why not?

Answer:

it is because 10 times 100 is 1000 so it would be the same thing

Step-by-step explanation:

Answer:

Paul's average speed for his bicycle trip is 12 miles/hour.

Step-by-step explanation:

Since Paul rode a total of 42 miles, we need to add up the total time it took him to complete all 42 miles.  Since her rode 1.5 hours in the morning and another 2 hours in the afternoon, he rode a total of 3.5 hours.  Speed is calculated by dividing distance by time.  Since his total distance is 42 and his total time is 3.5, we divide 42 by 3.5 to get 12.  Since our calculations included miles and hours, then our final answer would be 12 miles per hour.  

Answer:

There is one solution

Step-by-step explanation:

You can tell by looking at it that 2x and 3x are different. Both are obtained once the brackets have been removed. So you will get just one answer.

2(x -1) = 3(x - 4)                  Remove the brackets.

2x - 2 = 3x - 12                  Subtract 2x from both sides.

2x - 2x - 2 = 3x - 2x - 12   Combine

-2 = x -12                           Add 12 to both sides.

-2 + 12 = x -12 +12             Combine

10 = x

Answer:

x=71

Step-by-step explanation:

Since this is an isosceles triangle the bottom 2 angles are equal.

The three angles of the triangle are x, x, and 38.  They must add to 180 degrees

x+x+38 = 180

Combine like terms

2x+38=180

Subtract 38 from each side

2x+38-38 = 180-38

2x = 142

Divide each side by 2

2x/2 =142/2

x =71

Final answer:

The question hints at possible arithmetic or sign operation errors Lucia made while solving a system of equations. Pinpointing her exact mistake involves understanding common errors like incorrect handling of negative numbers or arithmetic operations.

Explanation:

The question involves identifying the mistake Lucia made when solving a system of equations. When solving for the value of x, there are various potential errors one could make, such as incorrect addition, subtraction, or misinterpretation of the operation sign. For instance, treating − 2( − 9) as 18 instead of − 18 is a common mistake due to misunderstanding how to handle double negatives in algebra. Similarly, when solving for the value of y, mistaking − 2y for 2y shifts the equation's balance, leading to incorrect solutions.

Lucia's error could stem from a few different places described in the question, but without the specific steps Lucia took, it's challenging to pinpoint the exact mistake. However, common errors to watch out for when solving for x and y in systems of equations include incorrect operations with negative numbers, improper handling of variables, or erroneous arithmetic operations.

Correctly solving a system of equations requires careful attention to each algebraic step, ensuring that operations on both sides of an equation are correctly applied and that signs are properly managed. Seeking to correct mistakes like treating negative signs improperly or misapplying arithmetic operations is essential for accurate solutions.

Answer:

[tex]-13a+22[/tex]

Step-by-step explanation:

we have

[tex]2(a+5)-3(5a-4)[/tex]

step 1

Apply the distributive property  both terms

[tex]2a+2(5)-3(5a)+3(4)[/tex]

[tex]2a+10-15a+12[/tex]

step 2

Combine like terms

[tex](2a-15a)+(10+12)[/tex]

[tex](-13a)+(22)[/tex]

[tex]-13a+22[/tex]

Answer:

Exponential growth; percentage rate of growth is 4%.

Step-by-step explanation:

The function,

[tex]f(x)=3.6.(1.04)^x[/tex]

represents an exponential growth function because the growth factor is greater than 1.

The general form of an exponential growth function is,

[tex]y=a(1+r)^t=(a).(ar)^t[/tex], where 'r' is the percentage rate of growth.

If we compare the given equation with the standard form of the equation we can see that, we have,

[tex]f(x)=3.6(1+0.04)^x[/tex]

Therefore, the percentage rate of growth is = [tex]0.04 \times 100=4\%[/tex] .

Answer: sir or ms your anwser would be C 98. hope this helps ;)

Step-by-step explanation:

Answer:

During WWII, 120,000 Japanese-Americans were forced into camps, a government action that still haunts victims and their descendants. ... The roundups began quietly within 48 hours after the Japanese attacked Pearl Harbor, on December 7, 1941. The announced purpose was to protect the West Coast.

hope this helps.

Step-by-step explanation:

Answer:if your still on it tell me

Step-by-step explanation:

By using the ratio and proportion method, it is calculated that 5 ladles of soup can feed 96 people.

This problem can be solved using the ratio and proportion concept in Mathematics. Given that 3 ladles of soup feed 160 people, we can set up the ratio 3 ladles : 160 people. If the cook now provides 5 ladles, we need to know how many people this amount can feed. To find this, we cross-multiply in the ratio.

Calculating: (3 ladles x X people) = (160 people x 5 ladles), after simplifying we find that X = 96 people. This calculation suggests that the soup will now feed 96 people if each person is given 5 ladles of soup.

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[tex]d(e-f)=g\\e-f=\frac{g}{d} \\e-\frac{g}{d}=f[/tex]

Steps:

Divide by D

Add F

Subtract g/d

Answer:

f = -g/d +e

Step-by-step explanation:

d (e-f) =g

Divide each side by d

d/d (e-f) =g /d

(e-f) =g /d

Subtract e from each side

e-e-f = g/d -e

-f = g/d -e

Multiply by -1

*-1 (-f) = -1(g/d -e)

f = -g/d +e

To find out how many days 1/3 of a packet of milk powder will last, divide 1/3 by 2 to get 1/6 of a day.

To find out how many days 1/3 of a packet of milk powder will last, we can use the information given. Kate uses 2 packets of milk powder per day. This means in one day, she uses 2 packets. So, in order to calculate how many days 1/3 of a packet will last, we need to divide 1/3 by 2. This gives us 1/6.

Therefore, 1/3 of a packet will last 1/6 of a day.

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1/3 of a packet of milk powder will last 1/6 of a day, or 4 hours, for Kate who uses 2 packets of milk powder per day.

If Kate uses 2 packets of milk powder per day, to determine how many days 1/3 of a packet of milk powder will last, you can perform a simple division. Since she uses 2 packets per day, you would divide the amount she has, 1/3 of a packet, by her daily usage, which is 2 packets. Therefore:

1/3  packets / (2 packets/day) = (1/3) / 2 days = 1/6 days

Thus, 1/3 of a packet of milk powder would last for 1/6 of a day. To determine the number of hours this represents, you can multiply 1/6 of a day by the number of hours in a day:

(1/6 day) times (24 hours/day) = 4 hours

Therefore, 1/3 of a packet of milk powder will last for 4 hours based on her current usage.

The statement which best describes the graph of g(x) is:

                Option: A

    A.  g(x) stretches f(x) vertically by a factor of 2.

We are given a original function f(x) as:

          [tex]f(x)=2\ln x[/tex]

and a transformed function g(x) as:

               [tex]g(x)=4\ln x[/tex]

We know that any transformation of the type:

  f(x) to a f(x) is a vertical stretch by a factor of a if a>1

and a vertical compression if a<1

Here we have:

[tex]g(x)=2\times (2\ln x)\\\\i.e.\\\\g(x)=2f(x)[/tex]

i.e. g(x) is a vertical stretch of f(x) by a factor of 2.

Answer:

Very confident

Step-by-step explanation:

The closer the correlation coefficient is to 1, the stronger the correlation.  Anything above .4 is relatively strong.    So I would be very confident.

Answer:

you save $52.11 by shopping at the second store

Step-by-step explanation:

The total sale price at the second store is $240.95.

additional 10% off coupon for the second store for purchases over $200.00

10% discount on sale price is 240.95 * 10%

[tex]240.95 * \frac{10}{100} = 24.095[/tex]

Total sale price after 10% discount =240.95 - 24.095=$216.86

First store sale price = $268.97

second store sale price = $216.86

Difference = 268.97 - 216.86 = 52.11

you save $52.11 by shopping at the second store

Answer: 11.88

Step-by-step explanation: First You Add 8.09 then you add 3.79 Therefore your answer is 11.88

Hope This Helps You Ace Your Test

Answer:

$70.77

Step-by-step explanation:

Let  represents the total cost. We know for our problem that each yard of satin fabric costs $8.09, so  yards will cost . similarly,  each yard of cotton fabric costs $3.79, so  yards will cost . We can also infer that the total cost, , will be the sum of the yards of satin fabric and the yards of cotton fabric, so:

Now, to determine the amount that Angeline would spend in all if she bought 5 yards of satin fabric and 8 yards of cotton fabric, we just need to replace  and  in our expression:

We can conclude that if Angeline would spend in all if she bought 5 yards of satin fabric and 8 yards of cotton fabric, she would spend $70.77

Answer:

Transformation that produces an image that is the same shape but different size is known as Dilation.

Step-by-step explanation:

There are many types of translations.

1. Rotation

2. Reflection

3. Translation

4. Dilation

We know that rotation, reflection and translation are rigid transformation. It means these transformation can not effect the size of the preimage.

Dilation represents the enlargement and compression of the figure according to the scale factor k.

If |k|>1, then it represent enlargement and if |k|<1, then it represent compression.

Therefore the transformation that produces an image that is the same shape but different size is known as Dilation.

Answer:

The percent increase is 34.48276%

Step-by-step explanation:

we are given

original price =$2900

new price =$3900

now, we can find change in price

change in price = (new price)-(original price)

change in price =3900-2900

change in price =1000

percent increase = (change in price)/(original price) *100

percent increase is

[tex]=\frac{1000}{2900}\times 100[/tex]

[tex]=34.48276[/tex]

Answer:

Solution point is (-1,-9)

Step-by-step explanation:

Put the value of y in the first equation into the second equation.

=======

Solve for y

Hi there!

Step-by-step explanation:

[tex]SLOPE=\frac{Y_2-Y_1}{X_2-X_1}=\frac{RISE}{RUN}[/tex]

[tex]\frac{2-4}{3-(-4)}=\frac{-2}{7}[/tex]

Slope is -2/7

Final answer is -2/7.

Hope this helps!

Have a nice day! :)

:D

-Charlie

Thank you! :)

:D

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points (-4, 4) and (3, 2). Substitute:

[tex]m=\dfrac{2-4}{3-(-4)}=\dfrac{-2}{3+4}=-\dfrac{2}{7}[/tex]

The slope-intercept form:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

We have the equation in standard form.

[tex]2x-3y=6[/tex]      subtract 2x from both sides

[tex]-3y=-2x+6[/tex]      divide both sides by (-3)

[tex]y=\dfrac{2}{3}x-2[/tex]

Answer:

C

Step-by-step explanation:

Arrange them from smallest x value to largest x value, but keep the values the same.

Final answer:

To divide 65.2 by 26, you perform the division to find that 26 goes into 65.2 exactly 2.5 times. Therefore, the answer, when rounded to the nearest tenth, is 2.5.

Explanation:

To divide 65.2 by 26, start with the division process. Place a decimal point directly above the decimal point in the dividend within the answer area. Since 26 does not go into 6, but goes into 65 twice, write 2 above the 5 in the dividend. Multiply 2 by 26 to get 52, and subtract this from 65, which leaves a remainder of 13. Bring down the 2 from the dividend to get 132.

Now, divide 26 into 132, which goes exactly 5 times. Multiplying 5 by 26 gives 130, subtract this from 132 to get a remainder of 2. Because we are left with no more numbers to bring down and our remainder is less than 26, we stop. The answer to 65.2 divided by 26 when rounded to the nearest tenth is 2.5.

Answer:

slope = [tex]\frac{9}{7}[/tex]

Step-by-step explanation:

to calculate the slope m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (- 6, - 3) and (x₂, y₂ ) = (1,6) ← 2 points on the line

m = [tex]\frac{6+3}{1+6}[/tex] = [tex]\frac{9}{7}[/tex]